Plasma oscillations and nonextensive statistics

The dispersion relations for electrostatic plane-wave propagation in a collisionless thermal plasma are discussed in the context of the nonextensive statistics proposed by Tsallis. Analytic formulas both for the undamped (Bohm-Gross) and Landau damped waves are derived and compared with the standard results. In the extensive limiting case $(q=1),$ the classical dispersion relations based on the Maxwellian distribution are recovered. It is shown that the experimental results points to a class of Tsallis's velocity distribution described by a nonextensive q-parameter smaller than unity.